A view through the walls of our classroom. This is an interactive learning ecology for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

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Monday, October 27, 2008

TEST RESULTS/REVIEW

I guess I ran out of creative titles for this scribe post, but it's a Monday. What can I do? Well, the majority of the time was spent dwelling on the little test we had. I'll put it lightly. MOTHER FATHER!!!! It was completely devastating...especially for my self expectations. It really brings me down you know?

Anyhow, I can't really re-explain the answers of the test considering that these tests were probably "recycled", so what I'll do is give reminders and notices for the important dates coming soon in class and maybe recap what I've learned in this chapter so far. So I won't have to guilt trip myself into scribing one more time. I'll...compensate for it. I guess that's the right terms for it.

IMPORTANT DATES:Nothing really comes to mind except the likely test we will have on Friday this week. Happy halloween. That's what makes it so scary. Not the gore, the blood, or the costumes; it's the tests.

.:. J + ME .:.'s REVIEW OF CHAPTER 3 [I'm warning you..not to rely on this, it's probably not very informative. I'm just doing this to see if I understand this stuff or not. It's an effort, right? Wow.. whatever happened to my skills in English? I'm writing so informally. **sigh**]

3.1 CALCULATING DISTANCE TRAVELEDThis is the first part of the chapter which acts as a link between the concepts of the previous chapter 2 and preparation for what will be taught further into the unit.

We discover that both integrals and derivatives have direct relationships with each other given that a derivative is a rate of change involving velocity and integrals involve determining the distance traveled, which is basically the area of the region below a function.

This chapter is easily explained remembering the idea of

distance = velocity x elapsed time.

3.2 CALCULATING AREAS: RIEMANN SUMSThis chapter focuses more on approximating the areas of rectangular regions below the functions and also parts of the regions above the function.

To find these areas, we take the limit of these approx. sums and find the area using the measurements of the intervals and the height of each interval that touches the function. The smaller the intervals are, the closer we are to being more exact in our approximates in area.

The name RIEMANN sums is just the name assigned to classify the method to find these sums.

Of course we have to take into account inscribed [below] and circumscribed [above] rectangles since, they do not fill in the spaces exactly.

Especially when looking for Riemann sums using something as obscure as a calculator, it makes it easier when we look for subintervals and choose midpoints [or left or right endpoints], so that it is easier to find what are known as RIGHT HAND SUMS [above fcn] and LEFT HAND SUMS[below fcn].

3.3 DEFINITE INTEGRALSIn this part of the chapter, a variation of the sigma notation is introduced, something that looks like a squiggly line. How fun to illustrate. But the subscripted and superscripted values are the coordinates of the main interval, represented by [a, b] in the examples. We are still finding the sum of course, and it is the sums within the vicinity of of the main interval given. There is an infinite amt of limits of the number of intervals between [a, b].

I'm a bit choppy on this part still, so I'm sorry. I don't want to mislead anyone.

But another thing worth noting is the distinguishable difference between MONOTONOUS fcns and NON-MONOTONOUS fcns.

Monotonous Functions: are functions that either increase or decrease, but never go both ways.

Non-monotonous Functions: These functions are capable of increasing and decreasing, resulting in an "unpredictable" function and thus, it's intervals that don't follow a specific pattern.

Well that's all from me tonight. Ummmmm. Who shall be dubbed the next scribe? Rence, I guess.

With great power comes great responsibility. - UNCLE BEN. haha wow. when will that ever get old?